Connections between qualitative dynamical models and the Frobenius-Perron operator

The paper concerns the discrete-event behaviour of quantised systems. As the state can only be measured through a quantiser, trajectory bundles have to be considered, which can be represented for autonomous systems by theFrobenius-Perron operator and for systems with inputs by the Foias operator. These operators can be written down in an explicit form only for a restricted class of systems. Hence, discrete approximations of these operators are used in systems analysis. The paper shows that these approximations are identical to the state transition functions of stochastic automata, which are used in process diagnosis and verification. This interesting connection between results from mathematical systems theory and the literature on hybrid control systems makes it possible to combine the results obtained in both fields.